Statistics Papers

Document Type

Journal Article

Date of this Version

2013

Publication Source

Journal of the American Statistical Association

Volume

108

Issue

501

Start Page

265

Last Page

277

DOI

10.1080/01621459.2012.758041

Abstract

This paper proposes a new test for testing the equality of two covariance matrices Σ1 and Σ2 in the high-dimensional setting and investigates its theoretical and numerical properties. The limiting null distribution of the test statistic is derived. The test is shown to enjoy certain optimality and to be especially powerful against sparse alternatives. The simulation results show that the test significantly outperforms the existing methods both in terms of size and power. Analysis of prostate cancer datasets is carried out to demonstrate the application of the testing procedures. When the null hypothesis of equal covariance matrices is rejected, it is often of significant interest to further investigate in which way they differ. Motivated by applications in genomics, we also consider two related problems, recovering the support of Σ1 − Σ2 and testing the equality of the two covariance matrices row by row. New testing procedures are introduced and their properties are studied. Applications to gene selection is also discussed.

Copyright/Permission Statement

This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of the American Statistical Association on 02 Jan 2013, available online: http://wwww.tandfonline.com/10.1080/01621459.2012.758041.

Keywords

extreme value Type 1 distribution, gene selection, hypothesis testing, sparsity

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Date Posted: 27 November 2017